modeling belowground water table fluctuations in the everglades

Modeling belowground water table fluctuations in the Everglades

Dario Pumo,1,2 Stefania Tamea,3 Leonardo Valerio Noto,1 Fernando Miralles‐Wilhem,4

and Ignacio Rodriguez‐Iturbe2

Received 17 November 2009; revised 7 September 2010; accepted 21 September 2010; published 25 November 2010.

[1] Humid lands, such as riparian zones, peatlands, and unsubmerged wetlands, areconsidered among the most biologically diverse of all ecosystems, providing a bountifulhabitat for a large number of plant and animal species. In such ecosystems, the water tabledynamics play a key role in major ecohydrological processes. The aim of the present studyis to test with field data a recent analytical model for the estimation of the long‐termprobability distribution of the belowground water table position in groundwater‐dependentenvironments. This model accounts for stochastic rainfall and processes such asinfiltration, root water uptake, water flow from/to an external water body, and capillaryfluxes. The water table model is tested using field data of groundwater levels recorded inthree different sites within the Everglades (Florida, USA). A sensitivity analysis of themodel to the soil and vegetation parameters is also carried out. After performing aprocedure to determinate appropriate model parameters for the three sites, the steady stateprobability distribution functions of water table levels predicted by the model arecompared to the empirical ones at both the annual and the seasonal time scale. The modelis shown capable to reproduce many features of the observed distributions althoughthere exist model predictions which still show some discrepancies with respect to theempirical observations. The potential causes for these discrepancies are also investigatedand discussed.

Citation: Pumo, D., S. Tamea, L. V. Noto, F. Miralles‐Wilhem, and I. Rodriguez‐Iturbe (2010), Modeling belowground watertable fluctuations in the Everglades, Water Resour. Res., 46, W11557, doi:10.1029/2009WR008911.

1. Introduction

[2] Wetlands are areas which are inundated or saturatedby surface water or groundwater at a frequency and durationsufficient to support a prevalence of vegetations typicallyadapted for life in saturated soil conditions. They are char-acterized as having a water table that stands frequently at ornear the land surface. Wetlands were initially consideredmarginal, and for this reason they have historically beenvictims of large‐scale draining efforts, but they are indeedfar more important in the biosphere than their limitedworldwide spread (almost 7% of the world’s ecosystems)would suggest [Mitsch and Gosselink, 2007]. Wetlands aredynamic, complex habitats, supporting high levels of bio-logical diversity. Their natural ability to filter and cleanwater, contributes to the efforts to ameliorate the everincreasing challenge of decreasing water pollution. Theimportance of wetlands is also linked to their role in pro-tecting coastlines from hurricanes and tsunamis, mitigating

flooding of streams and rivers [Costanza et al., 2008;Srinivas and Nakagawa, 2008]. In addition, wetlands providean immense storage of carbon that, if released with climateshifts, could accelerate those changes. For all these reasons,the scientific community is currently devoting much attentionto those crucially important ecosystems [e.g., Novitzki, 1979;Gilvear et al., 1989; Brinson, 1993; Ramsar ConventionBureau, 1996; Mitsch et al., 2009; Eamus, 2009].[3] Wetlands are groundwater‐dependent ecosystems

(GDEs), namely, ecosystems whose current composition,structure and function are reliant on a supply of groundwaterand that require access to groundwater to maintain theirhealth and vigor.[4] In GDEs soil‐climate‐vegetation mutual interactions

control and at the same time are influenced by the water tabledepth and the soil water content. Water table fluctuations andsoil moisture profiles in fact, play a fundamental role inmajor ecohydrologic processes, including infiltration, sur-face runoff, groundwater flow, land‐atmosphere feedbacks,vegetation dynamics, nutrient cycling, and pollutant trans-port. The ecohydrological approach to the study of wetlandsrepresents indeed a new frontier of scientific research pre-senting particularly challenging features because of theintermittency and uncertainty inherent to the rainfall regime,and as a consequence, the coupled stochastic dynamics of thesoil moisture and the water table depth.[5] In the recent past, such dynamics were mostly

investigated either in terms of mean seasonal water fluxes(mean precipitation, evapotranspiration, drainage), or throughmore detailed numerical simulations of the soil water balance

1Dipartimento di Ingegneria Idraulica ed Applicazioni Ambientali,Università degli Studi di Palermo, Palermo, Italy.

2Department of Civil and Environmental Engineering, PrincetonUniversity, Princeton, New Jersey, USA.

3Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili,Politecnico di Torino, Turin, Italy.

4Department of Civil and Environmental Engineering, FloridaInternational University, Miami, Florida, USA.

Copyright 2010 by the American Geophysical Union.0043‐1397/10/2009WR008911

WATER RESOURCES RESEARCH, VOL. 46, W11557, doi:10.1029/2009WR008911, 2010

W11557 1 of 20

http://dx.doi.org/10.1029/2009WR008911

[e.g., Feddes et al., 1988; Berendrecht et al., 2004; Yehand Eltahir, 2005]. Salvucci and Entekhabi [1994] studiedthe role of temporal variability, for different water tablepositions, on soil moisture time profiles via simulationsbased on the numerical integration of the governing equa-tions in the unsaturated zone. Their simulations consisted offorcing the surface of a one‐dimensional soil column,bounded at its base by a fixed water table, with the output ofa stochastic event‐based model of precipitation and potentialevapotranspiration. In a different work, the same authors[Salvucci and Entekhabi, 1995] proposed a numericalmethod to determine the equilibrium water table position andthe corresponding spatial structure of the mean recharge,discharge, evaporation, and surface runoff throughout ahillslope. Bierkens [1998] investigated the water tabledynamics by means of a model that numerically solves astochastic differential equation, assuming equilibrium soilmoisture conditions; in this modeling stochasticity is intro-duced in the water balance as a generic noise term. Kim et al.[1999] proposed a transient, mixed analytical‐numericalmodel to study the patterns of infiltration, evapotranspiration,recharge and lateral flow across hillslopes.[6] Numerical calculations of soil moisture dynamics and

their impact on vegetation are not always well suited for aneffective analysis of the interdependence of soil, vegetation,and climate drivers, especially when it is necessary toaccount for the stochastic nature of these processes. Thus itis important to try to describe such interdependence, asmuch as possible, via analytical formulations.[7] Most of the early analytical research in ecohydrology

has concentrated on arid and semiarid ecosystems [e.g.,Porporato et al., 2001; Rodriguez‐Iturbe and Porporato,2004], where productivity strongly depends on soil wateravailability and the effect of water table dynamics on veg-etation can be neglected; in such ecosystems, in fact, thewater table, because of its deepness, can often be assumedmostly inaccessible to the same vegetation [D’Odorico andPorporato, 2006]. The search for analytical solutions [e.g.,Rodriguez‐Iturbe et al., 1999; Laio et al., 2001] of thestochastic soil water balance equation suggests the use ofsimple models of soil moisture dynamics, which are able toaccount for the random character of precipitation along withthe pulsing character of soil moisture. Rodriguez‐Iturbe etal. [2007] highlighted the need of an analytical frameworkfor the study of the stochastic soil water balance in humidlands. Also, wetlands indeed can be considered water‐lim-ited environments, even if their dynamics are substantiallydifferent from those of arid and semiarid ecosystems[Naiman et al., 2005; Mitsch and Gosselink, 2007]. In thecase of wetlands, the hydrologic control on vegetation andmicrobial stress does not arise fromwater limitation but ratherarises most frequently from waterlogging conditions and theconsequent limitation on soil oxygen availability [e.g.,Kozlowski, 1984; Roy et al., 2000; Brolsma and Bierkens,2007; Bartholomeus et al., 2008]. At the same time plantsmay, in turn, affect the water table depth, as observed inseveral kinds of wetland [Dacey and Howes, 1984; Dubé etal., 1995; Roy et al., 2000; Wright and Chambers, 2002].[8] Ridolfi et al. [2008] developed a probabilistic frame-

work to investigate the coupled soil moisture–water tabledynamics in the case of bare soil conditions. In two recentpapers, Laio et al. [2009] and Tamea et al. [2009] proposed

a process‐based probabilistic model valid in the case ofvegetated soils having roots interacting with saturated andunsaturated zones. Since this model, specific for GDEscharacterized by belowground fluctuations of the water tableposition, has never been tested with real data, this paperaims to fill this gap. Confronting the model with data pro-vides clues as to what processes may be missing from theconceptual model. Moreover, comparison with field resultscould provide important indications to improve the model inthe future. The development of quantitative methods for thestudy of the stochastic water balance in wetland ecosystemscould enable new and important research avenues in eco-hydrology, for example providing a framework to under-stand the role of humid lands as filters for contaminatedstreams and aquifers and to investigate how hydrologicprocesses affect ecosystem productivity, the emergence ofplant water stress, interspecies competition, the stability andresilience of wetland plant communities, and the complexityand nonlinearity of vegetation successional dynamics.[9] In particular, the objective of this paper is to test the

model by Laio et al. [2009], relative to the probabilisticstudy of water table fluctuations, through its application todifferent sites located in southeast Florida (USA) within theEverglades National Park. After a preliminary description ofthe model and the three sites chosen for its application, asensitivity analysis of the model to the vegetation and soilparameters is performed. In particular, a Monte Carlomethod has been used to study the effects of different soilparameters on the model outputs. Once appropriate modelparameters have been fixed for each site, the model per-formances at both the annual and seasonal (two seasons: dryand wet) time scales are investigated, providing also pos-sible causes for some discrepancies between the modelpredictions and the field observations.

2. Description of the Model and the SitesConsidered

2.1. Analytical Modeling of Water Table Dynamics

[10] In this section, the basic concepts and assumptions ofthe analytical model are recalled, while for more detailedinformation, the reader is referred to the original papers byLaio et al. [2009] and Tamea et al. [2009].2.1.1. Water Balance Equation[11] The model developed by Laio et al. [2009] is foun-

ded on a simple process‐based soil water balance equationforced by stochastic precipitation. The water balanceaccounts for rainfall infiltration, water table recharge, plantwater uptake, capillary flux, groundwater flow, and couplingbetween water table fluctuations and soil moisture dynamicsin the unsaturated portion of the soil column.[12] Considering a positive upward vertical axis with

origin at the soil surface, one can identify with ~y(t) the depthof the water table, defined as the saturated surface at zeropressure head (Figure 1). The saturated capillary fringe isassumed to occupy a constant portion of soil above thewater table, having a thickness equal to ∣ys∣, where ys is the(negative) bubbling pressure head, or saturated matricpotential. Thus the surface separating saturated and unsat-urated soil lies at a depth y(t) defined as

yðtÞ ¼ ~yðtÞ � y s; ð1Þ

PUMO ET AL.: MODELING BELOWGROUND WATER W11557W11557

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[13] Since the model does not account for soil submer-gence and it is limited at y ≤ 0, the shallowest water tableposition which can be captured lies at a depth ys below thesoil surface.[14] The soil matric potential, y(s), and the unsaturated

hydraulic conductivity, k(s), are related to the soil moisture,s, through the Brooks and Corey [1964] model truncated atsmall values of hydraulic conductivity (with k(s) = 0 for s ≤sfc). The value of the field capacity, sfc, is obtained byimposing k(sfc) = 0.05 PET, where PET is the potentialevapotranspiration rate.[15] Considering a homogeneous soil column at the plot

scale (e.g., 100 m2), the water balance equation with respectto the separation surface, y, can be written as

�ðyÞ � dy tð Þdt

¼ Reðy; tÞ � flðyÞ � UsðyÞ � ExðyÞ ð2Þ

where b(y), Re(y), fl(y), Us(y) and Ex(y) are the specificyield, the recharge rate, the lateral flow from/to an externalwater body, the root uptake from the saturated zone and theexfiltration from the water table due to the capillary flux(Figure 1), respectively.[16] Three different zones can be identified in the soil

column: the saturated zone, the unsaturated zone with highmoisture and the unsaturated zone with low moisture. At acertain time, t, the saturated zone (C in Figure 1) lies belowthe depth zsup = y(t), and has all the soil pores filled withwater, i.e., soil moisture s = 1. The high‐moisture unsatu-rated zone (HMUZ, B in Figure 1) has a soil moistureranging from field capacity (sfc) to saturation (s = 1) and, at acertain time t, is delimited by the depth zinf = y(t) and eitherthe soil surface (zsup = 0), if this is wetter than field capacity,or the depth zsup = h(t) (where h(t) is the depth of the layer atfield capacity at the time t), if the soil moisture content at thesuperficial layers is lower than sfc. The low‐moistureunsaturated zone (LMUZ, A in Figure 1) is present when-ever the upper part of the soil column has a soil moisturebelow field capacity and, at a certain time t, it lies betweenthe soil surface (zsup = 0) and the depth zinf = h(t). The depthh(t) depends on the steady state soil moisture profile and is adirect function of the water table position, as given byintegration of the local soil water balance in the unsaturated

soil (Richards equation). A stepwise function has beenproposed by Laio et al. [2009] to approximate the relationh(y), and the robustness of this approximation has been testedby the same authors for different soils and plant rootingdepths through a comparison with the numerical solution.[17] The model considers two different regimes: shallow

water table (SWT) and deep water table (DWT). The criticaldepth yc of the separation surface between the saturated andthe unsaturated zone corresponding to h(t) = 0, marks thetransition between these two regimes. The SWT regime ischaracterized by the absence of the LMUZ and occurswhenever y(t) > yc; otherwise the regime is that of DWT.The critical depth yc can be determined by integrating theRichards equation in steady conditions; since an analyticalsolution is not available, Laio et al. [2009] suggest the useof an approximate solution which is found to agree wellwith the solution obtained numerically for different types ofsoil and vegetation.[18] The recharge rate term, Re(t), represents the process of

groundwater recharge, which is the result of rainfall infil-tration and redistribution through the soil column. Rainfall atthe daily level is the stochastic forcing of the dynamic sys-tem. Here, following previous studies [Rodriguez‐Iturbeet al., 1999; Laio et al., 2006], the net rainfall reachingthe soil after canopy interception is assumed to be wellrepresented by a stationary marked Poisson process withrate l0. The marks correspond to independent and expo-nentially distributed daily rainfall depths with mean a. InSWT conditions, the rainfall frequency equals the rechargefrequency with all the rainfall coming into the HMUZcontributing to recharge. The process of infiltration andwater redistribution in the HMUZ are considered to occurinstantaneously, at the daily time scale, because soil mois-ture values are larger than the field capacity [Laio et al.,2006; Botter et al., 2007]. In DWT conditions, not all therainfall events reach the water table, and the LMUZ acts as abuffer which reduces the frequency of recharge events. Thenew frequency depends on the water table position, rainfalldepth and the soil moisture content in the LMUZ. In fact,assuming that all rainfall events find the same average soilmoisture content in the LMUZ, the sequence of the rechargeevents retains the Poissonian properties of rainfall occur-rences [Laio, 2006] and the recharge rate will not depend on

Figure 1. Schematic representation of the terms of the water balance equation and variables involved inthe evaluation of the lateral flow [after Laio et al., 2009].


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the fluctuations of s(z) but only on the local long‐termaverage values. The recharge process has thus a mean deptha and a rate l(y) given by

�ðyÞ ¼ �0 �!SWT

�ðyÞ ¼ �0 � expn � hðyÞ � sfc � sm0 hðyÞð Þ� �

�

� ��!DWT

8><>: ð3Þ

where l0 is the rate of net rainfall occurrences (e.g., afterinterception is accounted for), h(y) is the depth of theboundary layer between the HMUZ and the LMUZ ands′m(h) is the long‐term average soil moisture in the LMUZ[Tamea et al., 2009].[19] The lateral flow fl in equation (2) takes into account

the presence of a nearby water body or a regional ground-water level, and it depends on the relative position of thelocal water table, ~y, and the free surface of the external waterbody. The external water body has a water surface at thedepth y0 (Figure 1), relative to the soil surface at the siteunder consideration, which is constant in time. The externalwater body is located at a distance from the site which islarge enough to assume a horizontal water table at the siteunder analysis. The lateral flow can then be described by alinear relationship, similar to Darcy’s law, for both the SWTand DWT conditions:

fl yð Þ ¼ kl � y0 � y� y sð Þ ð4Þ

where kl is a constant of proportionality, whose estimationwill be discussed in section 3.2.[20] In the water balance equation the effect of evaporation,

which is small compared to transpiration when a dense veg-etation cover is present [Laio et al., 2009], is neglected. Theterms Us and Ex in the water balance equation (equation (2))represent the water losses from the saturated zone due toroot uptake and capillary rise (exfiltration), respectively. Thefirst term represents the effect of water uptake by rootsallocated within the saturated zone while the second term isthe upward vertical movement of water from saturated topartially saturated soil layers, due to capillary rise that, inturn, is driven by the difference in soil matric potential in thesoil layers induced by plant water uptake, and thus depen-dent on the location and distribution of the roots.[21] The model by Laio et al. [2009] considers three

simplifying assumptions on the functioning of root uptake.The first assumption is that the uptake flux is unaffected byanoxic (saturated) conditions in the soil and, then, nouptake‐reduction function is applied for large values of s.This assumption is justified by the fact that most of the plantspecies populating humid lands are well adapted to soil

anoxic conditions and can cope with saturation conditionsadopting different strategies to survive waterlogging. Forexample, they may develop anaerobic metabolisms and thus

be able to increase oxygen provision to the roots [e.g.,Naumburg et al., 2005; Vartapetian and Jackson, 1997].The second assumption is that a noncooperative root func-tioning system is considered neglecting compensation me-chanisms [see, e.g., Guswa, 2005, 2008]. Thus, roots in eachsoil layer are considered to take up water independently ofthe others, without compensating for limitations in transpi-ration and uptake, which may occur somewhere along thesoil profile. Finally, the third assumption is that the plot‐scale averaged root distribution can be represented by asimple normalized function r(z). Following other authors[e.g., Schenk and Jackson, 2002; Schenk, 2005], an expo-nential distribution of the root biomass, r(z) = 1/b · e

z=b, isconsidered, where b is the average rooting depth. With theseassumptions, the root uptake, U(z), at the generic depth z,within the saturated zone, is directly proportional to the rootdensity r(z) and the maximum potential evapotranspirationrate, PET (which is controlled only by atmospheric condi-tions). Then, the total root uptake from the saturated zone(for both the cases of SWT and DWT) reads

UsðyÞ ¼ PET � eyb ð5Þ

[22] The exfiltration term, Ex, takes into account themechanism of capillarity due to vertical gradients of soilmatric potential induced by plant transpiration. FollowingLaio et al. [2009], the term in the water balance equation forthe cases of shallow and deep water table regimes, can bewritten as

ExðyÞ ¼ PET � 1� eyb

� � �!SWT

ExðyÞ ¼ PET � ehb � e

yb

� �!DWT

8><>: ð6Þ

[23] From equations (5) and (6), one can note that, underSWT conditions, the total flux from the saturated zone,leaving aside the lateral flux, (i.e., Us + Ex), is constant andequal to the potential evapotranspiration rate. It is assumedthat for s < sfc, the hydraulic conductivity is null, then, thedepth h (where s = sfc) also represents the threshold abovewhich the water table exerts no influence on the local soilwater balance and, as a consequence, no capillary fluxes arepresent in the LMUZ.[24] Finally, the specific yield, b(y), in equation (2)

converts the volumetric fluctuations (positive or negative)of water within the aquifer in the corresponding fluctuationsin water table position. It depends on the water table depthand on the soil properties, as well as on the SWT or DWTcondition. The specific yield was obtained by Laio et al.[2009]as

�ðyÞ ¼ n� n 1þ s� 1

2mfc � 1

� � y

yc

�� 2m

�!SWT

�ðyÞ ¼ n 1� sfc� �þ n � dh

dy� 1

�� 1

2m� 1� 1� sfc

1� s12mfc

� 2msfc þ sfc � 1

0@

1A �!DWT

8>>>>><>>>>>:

ð7Þ

where n is the porosity, m is the pore size index [Brooks andCorey, 1964], and dh/dy is the derivative of the h(y) rela-tionship given by Laio et al. [2009].


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2.1.2. Probability Distribution of the Water TableDepth[25] The model provides the stationary probability density

function of the depth y of the surface marking the separationbetween saturated and unsaturated soil. It is possible torewrite the soil water balance equation as

dy

dt¼ f ðyÞ þ gðyÞ � �ðy; tÞ ð8Þ

where the terms f (y), g(y) and x(y) are

f ðyÞ ¼kl y0 � y� ysð Þ � PET

�ðyÞ �! SWT

kl y0 � y� ysð Þ � PET � ehðyÞ=b�ðyÞ �! DWT

8>>><>>>:

gðyÞ ¼ 1

�ðyÞ

�ðy; tÞ ¼P �0; �ð Þ �! SWT

P �0 � expn � hðyÞ � sfc � sm0 ðhðyÞÞ

� ��

� �; �

��! DWT

8><>:

ð9Þrespectively.[26] The above stepwise continuous first‐order stochastic

differential equation can be solved under steady state con-ditions. The solution for the case of a state‐dependent noiserate l(y) is given by D’Odorico and Porporato [2004] andPorporato and D’Odorico [2004] as

pY ðyÞ ¼ C

f ðyÞ � ��ðyÞgðyÞ

� exp �Zy

0

f ðyÞ� � gðyÞ � f ðyÞ � ��ðyÞgðyÞ½ � du

24

35 ð10Þ

where C is a normalization constant obtained by settingR0�1

pY(y) = 1. The probability density function of the water

table depth, ~y, is obtained with a simple translation, andreads: p

~Y(~y) = pY(y + ys).

[27] The pdf of y (equation (10)) ranges from the soilsurface, where the probability goes to zero, to the lowerbound, ylim, representing the deepest position allowed by themodel. This can be computed from the steady state waterbalance in the absence of rainfall [Laio et al., 2009], i.e.,fl(ylim) = Us(ylim) + Ex(ylim). As a consequence of thesebounds, the pdf of the water table position ranges from ys to~ylim (equal to ylim + ys).

2.2. Description of the Sites

[28] The dense monitoring network covering the Ever-glades (Florida, USA) makes this areas an ideal location totest the model in virtue of the abundance of publiclyavailable data sets (e.g., water table depths, rainfall,evapotranspiration, soil and vegetation properties, etc.)having long series of daily measurements. Some of the mostimportant agencies monitoring the Florida Evergladestogether with their Web links, frequently referred to in thispaper, include the following: U.S. Geological Survey

(USGS, http://www.usgs.gov); Everglades Depth EstimationNetwork (EDEN; http://www.sofia.usgs.gov/eden); FloridaCoastal Everglades‐Long‐term Ecological Research (FCE‐LTER; http://www.fcelter.fiu.edu); South Florida WaterManagement District (SFWMD; http://www.sfwmd.gov).[29] In particular, we choose three different sites where

long historical series of daily data of groundwater depths,precipitation and evapotranspiration are available. Much ofthe Everglades landscape is subject to extended and pro-longed flooding, especially during the wet season (fromJune to November). Since the model does not account forstanding water, the sites have been chosen among thosehaving water level fluctuations within the shallow soil layerin order to warrant that submergence of the sites is limited intime or not occurring. For this reason, the three sites chosenare only partially representative of the general conditions ofwater level fluctuations in the Everglades.[30] All the sites are located in southeast Florida (USA),

Dade County, within the Everglades National Park (Figure 2).Site 1 is located in the Florida Bay, very close to the sea.The gauging station is named Taylor River at Mouth (aliasTS/Ph‐7a), and the operating agency is the USGS. The data ofgroundwater levels, rainfall and potential evapotranspirationare available at the EDEN, USGS and FCE‐LTERWeb sites.The site, located within the Taylor Slough watershed, pre-sents flat topography, with a tidal creek and limestone bed-rock. The shallowest portion of soil is made up of wetlandpeat (>1 m thick) while the vegetation is mangrove.[31] Site 2 is located within the so‐called Frog Pond Area,

between the canal C111 and the levee L31W. The ground-water well, identified by the code FRGPD2, is operated bySFWMD, and the data are available at their Web site. Forprecipitation and evapotranspiration data, the station con-sidered is the L31W (alias TS/Ph‐1b), managed by ENP(Everglades National Park), with data available at the EDENWeb site. This weather station is almost 2 km from thegroundwater well FRGPD2. This site is also located withinthe Taylor Slough watershed, and is characterized by flattopography and limestone bedrock. The shallower soil iswetland marl and the vegetation is mainly sparse sawgrass.[32] Site 3 is located near the levee L31W, close to the

northern area of the Taylor Slough. The groundwater well isR158G and the operating agency is the ENP. Groundwaterdata are available at the SFWMDWeb site. For precipitationand evapotranspiration data, the station considered is TS2(alias TS/Ph‐2), managed by ENP, with data available at theEDEN Web site; this station is located about 2 km from thestation R158G. The topography of the area is flat and thegeology is characterized by limestone bedrock. The soilpresents a layer of wetland marly peat (about 1 m thick) andthe vegetation cover is sparse sawgrass.[33] In the evaluation of the lateral flow contribution, it is

important to point out that for Site 1, the closest externalwater body is the ocean, while for the other two sites thecloser external water bodies are large canals (C111 andL31W), where daily records of water levels are also avail-able. These canals are part of the water management systemdeveloped in the South Florida throughout most of the 20thcentury. The canals were initially conceived as drainagecanals, with small success for their original purpose. Theinitial impact of the canal network on the Evergladesgroundwater was that of lowering the water table thus cre-ating a hydraulic gradient between the Everglades and the


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Atlantic Ocean that caused an unexpected increase ofmarine intrusion. For this reason, the most recent engi-neering works have been addressed toward the reestablish-ment of the natural conditions of the water levels within theEverglades. Canals and levees construction expandedgreatly during the 1950s and 1960s, reaching its final phasein the 1980s, with the completion of the Everglades‐SouthDade conveyance system [Renken et al., 2005].

2.3. Analysis of the Historical Data Series of WaterTable

[34] The ground elevation for each site has been derivedfrom the National Map Seamless Server provided by theUSGS, having a resolution of approximately 30 m. Thehorizontal datum is the NAD83 (North American Datum of1983) while the vertical datum is the NAVD88 (NorthAmerican Vertical Datum of 1988). The ground elevationsfound at the three sites are shown in Table 1.[35] Table 1 gives for each site the observation period, the

mean annual groundwater depths below the soil surface, aswell as the mean seasonal water table positions during thewet and dry season. Figure 3 shows the time series of water

table depths measured in cm and referred to the NAVD88;the original data for Sites 2 and 3 were referred to theNGVD29 (North American Geodetic Datum of 1929), thusthey have been converted to the NAVD88 with the verticalconversion factors provided by the EDEN Web site for thenearby stations L31W (Site 2) and TS2 (Site 3). The threetime series clearly show strong seasonality, mainly driven byrainfall: the water table is shallower during the wet season(from June to November) when most of the precipitationoccurs, while it lies in deeper layers during the rest of theyear. The behavior of groundwater fluctuations in Figures 3a,3b, and 3c, also shows the presence of some periods ofinundation which are relatively short and not very numerous,and thus not crucial for the purposes of this paper.[36] Figure 4a (left), Figure 4b (left), and Figure 4c (left)

show the autocorrelation functions (ACF) of the historicalwater table data relative to the three sites. The ACFs high-light the strong seasonality of the water level time serieswith a period of 365 days. The seasonality has beenremoved from each series by subtracting the mean dailygroundwater level throughout the years from each dailyvalue. This procedure allows one to obtain the time series ofwater table fluctuations around the mean value (referred to

Table 1. Information About the Groundwater Measurements at the Three Sitesa

Site 1 Site 2 Site 3

Ground elevation (m a.s.l.) (NAVD88) 0.10 1.09 0.83Water table measurement station TS/Ph7a FRGPD2 R158GOperating agency USGS SFWMD ENPWater table observation period 2 Oct 1995 to 26 Jan 2009 11 Oct 1996 to 14 Jan 2009 1 Oct 1983 to 3 Nov 2003Mean water table depth (annual) (cm) −30.3 −44.6 −52.1Standard deviation (annual) (cm) 8.7 18.2 19.5Mean water table depth (dry season) (cm) −34.6 −54.8 −61.3Standard deviation (dry season) (cm) 7.9 16.2 18.5Mean water table depth (wet season) (cm) −25.4 −34.1 −41.0Standard deviation (wet season) (cm) 6.9 13.7 14.3

aGround elevations in meters above the sea level (NAVD88). Dry season from December to May; wet season from June to November. Measurements incm below the soil surface.

Figure 2. Locations of the three sites used for the application of the model.


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Figure 3. Time series of water table levels and ground elevation for (a) Site 1, (b) Site 2, and (c) Site 3.Elevations are in centimeters above the North America Vertical Datum 1988.


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here as detrended series) whose ACFs (Figure 4a, middle;Figure 4b, middle, Figure 4c, middle) show less relevantpeaks without strong periodicity. One can notice that thedetrended ACF for Site 1 (Figure 4a) is rather different fromthose of the other sites (Figures 4b and 4c) with Sites 2 and3 maintaining higher correlation values in the detrendedseries. This could be due to the different nature of theinfluence of the external water body on the dynamics ofthe water levels; as mentioned above, in the case of Site 1 theclosest water body is the ocean while the other two sites arecontrolled by canals. The seasonal component of the oceaninfluence is more regular and thus more effectively removedafter detrending procedure. The presence of high correlationvalues in the detrended series for Sites 2 and 3 may in factresult from the human management of the nearby canals.

[37] The Power Spectra Functions (PSF) of the originaldata in the three case studies are shown in Figure 4a(right), Figure 4b (right), and Figure 4c (right), whichalso show their slopes (sl), in double logarithmic graphs,evaluated via least squares applied to the highest fre-quencies. The slopes corresponding to the detrended seriesare also given and, as expected, are very similar to theoriginal ones. One can notice that the largest value ofthe PSFs occurs at frequency of 10−2.56, corresponding tothe annual cycle (e.g., 1/365 days−1).

3. Estimation of the Model Input Parameters

[38] The average annual rainfall in South Florida variesfrom 120 to 160 cm, depending upon location [Lodge,

Figure 4. (a) Site 1, (b) Site 2, and (c) Site 3. Autocorrelation function (ACF) for (left) the original watertable series and (middle) for the detrended series after the removal of the seasonal cycle (ACF – DS).(right) The power spectra functions (PSF) for the original series, with the slopes marked in red. The slopesin green refer to the detrended series.


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2004]. In an average year, about 60% of the rainfall falls inthe 4 month summer period of June through September, andonly 25% falls in the 6 month dry season from Novemberthrough April. May and October are pivotal months withinconsistent rainfall. According to FCE‐LTER the localclimate at the three sites chosen is subtropical moist withdistinctive wet (June–November) and dry (December–May)seasons. In this study, two different parametric aggregationschemes are investigated: annual and seasonal. In the annualanalysis the model uses as input parameters the averageannual values for the potential evapotranspiration, for therainfall parameters (mean depth and frequency) and for theelevation of the water surface in the nearest external waterbody. In the seasonal analysis, following the FCE‐LTERsubdivision of the hydrological year, the model considerstwo different seasons, each one having its own set of inputparameters: dry season (from December to May) and wetseason (from June to November). The two different sche-matizations (annual and seasonal) consider the same soil andvegetation parameters (time invariant quantities).

3.1. Rainfall and Evapotranspiration

[39] The climatic forcings that the water balance modelrequires are the daily potential evapotranspiration rate andthe two rainfall parameters: daily mean depth a and inter-arrival rate l. The EDEN Web site provides historical seriesof rainfall and potential evapotranspiration useful for thegeneration of such climatic parameters.[40] Rainfall data based on Next Generation Radar

(NEXRAD) provide a complete spatial coverage of rainfallamounts for the State of Florida. The NEXRAD coveragefor the South Florida Water Management District area in-cludes rainfall amounts at 15 min resolution intervals for theperiod 1 January 2002 to present with a spatial resolution of2 km (EDEN Web site). The daily rainfall series consideredfor the three sites cover the period from 01/01/2002 to 09/30/2008. The annual and seasonal values of a and l ob-tained from the series in the three different sites are sum-marized in Table 2.[41] Daily potential evapotranspiration (PET) estimates

on a 2 km resolution grid have been produced by EDEN forthe State of Florida by means of a model that uses solarradiation obtained from Geostationary Operational Envi-ronmental Satellites (GOES) and climate data coming fromthe Florida Automated Weather Network, the State ofFlorida Water Management Districts and the NationalOceanographic and Atmospheric Administration (NOAA).Daily PET values (in millimeters) are then extrapolated bylocation for each of the EDEN stations and published at the

EDEN Web site. The daily series of potential evapotrans-piration considered in this work for the three sites are from06/01/1995 to 12/30/2007. Table 2 shows the mean dailyvalues of potential evapotranspiration during the year andduring the two seasons, for each site.[42] From Table 2 it is possible to note that, for the

considered sites, about 75% of the average annual precipi-tation is concentrated during the wet season, when theaverage values of potential evapotranspiration are about24% higher than in the dry season.

3.2. Parameters for the Lateral Flow Evaluation

[43] The lateral flow term (equation (4)) requires twoparameters to be estimated: y0 and kl. The model parametery0 corresponds to the depth of the free surface in the nearestwater body from the site, measured with respect to the soilsurface at the same site, and it is assumed to be constant intime, while kl is the proportionally constant for the saturatedlateral flow.[44] In the case of Site 1, the external water body is the

ocean (with a distance from the site of almost 70 m) and y0corresponds to the opposite of the ground elevation at thesite (same absolute value but opposite sign). For Sites 2 and3 the nearest water bodies are two different water canalswith available measurements of daily water levels. Thereference elevations y0 are taken as constant and equal to themean annual value for the annual analysis and to the meanseasonal values for the seasonal analysis. At Site 2, thenearest water body is canal C111 (with a distance from thesite of near 410 m), whose historical daily series of waterlevels recorded at station S176H has been used. For Site 3the nearest canal is levee L31W (almost 370 m from thesite), with a gauging station (S175H) about 2 km from thegroundwater well. The observation periods, the mean annualand seasonal values of the water levels in the canals, theground elevations and the resulting annual and seasonalvalues of y0 for both sites are summarized in Table 3.[45] The model parameter, kl, can be evaluated by means

of an inverse procedure involving the time series of mea-surements of the water table depths. With a long seriesrepresentative of the long‐term behavior of the water tablefluctuations, one can assume the value of ~ylim (i.e., thedeepest position allowed by the model; see section 2.1.2) asbeing equal to the deepest position of the water table re-corded during the observation period, ~ymin, corresponding tothe position of the water table after the longest dry period (inabsence of rainfall). The value of kl can then be computedfrom the steady state water balance in the absence of rainfall(i.e., fl(ymin) = Us(ymin) + Ex(ymin)), by using equations (4),

Table 2. Mean Annual and Seasonal Values of the Rainfall Parameters Depth a, Frequency l, and Total Precipitation Amount Q andPotential Evapotranspiration (PET)a

Site

WeatherStation

Associated(EDEN)

Rainfall

PET(cm/d)

Rainfall

PET(cm/d)

Rainfall

PET(cm/d)

a(cm)

l(1/d)

Q(cm/yr)

a(cm)

l(1/d)

Q(cm/yr)

a(cm)

l(1/d)

Q(cm/yr)

1 Taylor Riverat Mouth

0.79 0.347 99 0.42 0.62 0.206 23 0.37 0.86 0.491 77 0.46

2 L31W 0.82 0.431 130 0.38 0.71 0.245 32 0.34 0.87 0.621 99 0.423 TS2 0.79 0.414 119 0.39 0.70 0.244 31 0.35 0.83 0.588 89 0.43

aDry season from December to May; wet season from June to November. The weather stations are managed by SFWMD, and the data are available atthe EDEN Web site (http://www.sofia.usgs.gov/eden).


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(5) and (6) with y = ymin. It is important to point out that hisprocedure requires the preliminary computation of the soiland vegetation parameters and thus the obtained values of klare related to the evaluation of these parameters.

3.3. Vegetation Parameters

[46] The dominant vegetation within the Everglades isconstituted by sawgrass, specifically called Jamaica swampsawgrass, although many other marsh plants are also presentin the region [Lodge, 2004]. In the sites under study, thevegetation is mainly made up by mangrove at Site 1 and bysparse sawgrass at Sites 2 and 3 (FCE‐LTER). Sawgrassvegetation in the Florida Everglades includes species suchas Claudium jamaicense, Eleocharis cellulose, E. elongata,E. interstincta and Panicum hemitomon. Sawgrass is acoarse, rhizomatous, perennial sedge. Often it grows indense, nearly monospecific stands which result from anextensive network of rhizomes. Apical meristems arise fromthe top of the rhizomes. In the Everglades, Yates [1974]found that rhizomes were generally within the top 10 cmin marl soil, and within the top 15–20 cm in peat.[47] Mangrove vegetation in South Florida includes

species such as Rhizophora mangle, Avicenna germinas,Laguncularia racemosa and Conocarpus erectus. Some ofthe main features and botanical characteristics of this speciesare provided by Little [1983] and the U.S. Forest ServiceWeb site (http://www.fs.fed.us). Mangrove is usually anevergreen shrub 1.5 to 4 m tall which sometimes can also bepresent as a tree (for species such as Avicenna germinas andLagunaria racemosa) with heights up to 12 m (vegetation atSite 1 is classified as mangrove with low stature). The rootsystem consists mainly of laterals and fine roots that are darkbrown, weak and brittle, and have a corky bark (Conocarpuserectus). Mangroves are an example of salt‐resistant halo-phyte which have special features (adaptations) allowingthem to cope with their difficult environment. The threemain ways that mangroves deal with the problem of toomuch salt are the following: (1) by eliminating it throughspecial salt‐secreting glands in their leaves, (2) by storing itin leaves and stems that are shed at the end of the growingseason, and (3) by keeping it from entering their cells by

means of special membranes in their roots. This fact explainsthe presence of this kind of vegetation in tidal areas, as in thecase of Site 1, and justifies the lack of consideration of salteffects in the model being used.[48] The model by Laio et al. [2009] assumes an expo-

nential distribution of the roots into the soil. Using theinformation available on the vegetation cover of the threesites, the parameter b (average rooting depth, equation (5))has been assumed equal to 12 cm for the mangrove vege-tation (Site 1) and 10 cm for the sawgrass (Sites 2 and 3).This assumption is not critical since, as it will be shown insection 4.1, the influence of the average rooting depth on thegeneral behavior of the pdf’s of water table depth is weak inthe cases studied here. With these parameters, the modelconsiders the root biomass concentrated mainly within thetop 17–20 cm of the soil (about 80% of the total root bio-mass), while only 5% of the total biomass is deeper than 31–37 cm (with the lower values referring to sawgrass while thehigher ones to mangrove).

3.4. Soil Parameters

[49] In this section some soil properties at the three sitesare discussed with the aim of finding appropriate ranges forthe model parameters. These will then be used in the sen-sitivity analysis of the model results, which will be pre-sented in section 4.[50] Two soil types are usually present in the Florida

Everglades: marl and peat. Marl is the main soil of the short‐hydroperiod wet prairies near the edges of the southernEverglades while peat is more common in Evergladesmarshes (Everglades peat and Loxahatchee peat). In par-ticular, Everglades peat is made up almost entirely of theremains of sawgrass [Lodge, 2004].[51] The existing body of knowledge concerning peat soil

is not as large as that concerning mineral soil. However, inrecent years, there has been increasing interest about wet-lands [Hoag and Price, 1995] which encouraged anincreasing number of analysis focused on the hydraulicproperties of peat [Boelter, 1965; Ingram, 1967; Hoag andPrice, 1995; Holden and Burt, 2003; Rizzuti et al., 2004;Rosa and Larocque, 2008]. Almost all the studies agree inthe fact that the characteristics of peat strongly depend onthe nature of peat, in terms of organic matter fraction andbotanical composition.[52] Peat must contain no more than a certain amount of

inorganic content (20% is a typical value [see Myers,1999]). The ash content (or mineral content) for the Ever-glades soils usually ranges from about 25% to 90%; how-ever, despite this high percentage of mineral content, itbehaves hydrologically as peat [Myers, 1999]. Porosity inpure peat is high if compared to that of mineral soils. As thepercentage of peat in a mixture peat‐mineral soil increasesfrom zero to 100%, the porosity increases from 40% to 90%[Boggie, 1970; Myers, 1999; Walczak et al., 2002].[53] A generic soil classification at the three sites under

analysis is given by the FCE‐LTER Web site. The soil atSite 1 is classified as wetland peat, at Site 2 the soil iswetland marl, and at Site 3 is wetland marly peat. The FCE‐LTER Web site provides also the fraction of organic matterin the three sites: 22% (Site 1); 14% (Site 2); 25% (Site 3).Thus, according to the relation porosity‐peat fraction pre-sented by Myers [1999], the porosity in the three sites

Table 3. Mean Annual and Seasonal Water Levels in the C111and L31W Canals and Annual and Seasonal Values of the ModelParameter y0 for Sites 2 and 3a

Site 2 Site 3

Water canal C111 L31WWater level measurement station S176H S175HOperating agency SFWMD SFWMDWater level observation period 1 Jan 1978 to

30 Jun 200717 Jun 1970 to8 Jul 1997

Water levels (m a.s.l.) (NAVD88)Annual 0.83 0.56Wet season 0.91 0.73Dry season 0.75 0.37

y0 (m)Annual −0.26 −0.27Wet season −0.18 −0.08Dry season −0.36 −0.46aThe y0 values are in meters below the soil surface for each site. For Site 1,

the nearest water body is the ocean, and y0 is simply the opposite of theground elevation (−0.10 m). Dry season from December to May; wetseason from June to November.


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should vary within the range from 0.45 to 0.53 (Site 3). Forthe sensitivity analysis of the model to the soil parametersthat will be discussed in section 4, a slightly wider range ofporosity, n, is investigated taking into account values from0.40 to 0.55.[54] Many researchers [e.g., Boelter, 1965; Ingram, 1967;

Sturges, 1968; Dai and Sparling, 1973; O’Brien, 1977;Chason and Siegel, 1986] have attempted to measure thesaturated hydraulic conductivity of wetland soils using tra-ditional methods and found values ranging from 10−1 to10−7 cm/s, with most of the values falling between 10−3 and10−5 cm/s (i.e., from 1 to 85 cm/d). After a series of tests onundisturbed soil samples within southern Florida, Myers[1999] found values of the saturated hydraulic conductiv-ity ranging from 0.63 to 25.92 cm/d. These values are alsoquite close to those obtained for peat samples by otherauthors from laboratory analysis [Naasz et al., 2005;Katimonand Melling, 2007]. From these considerations, for the sen-sitivity analysis the parameter ks (i.e., saturated hydraulicconductivity) has been assumed potentially ranging from 0.5to 40 cm/d.[55] It is important to point out that the model developed

by Laio et al. [2009] assumes the soil column to behomogeneous and isotropic. Actually, the pure peat porositydecreases as the depth increases reaching an almost constantvalue in the catotelm zone (deeper layer with a well‐decomposed peat) while the hydraulic conductivity of theacrotelm (shallower layer commonly between 0 and 20 cmand made up of undecomposed dead plant material) hasbeen found to be up to five orders of magnitude greater thanthat of the catotelm [Boelter, 1965]. Moreover, pure peatpresents a strong anisotropy in hydraulic conductivity withhorizontal conductivity usually greater than the vertical one[Weaver and Speir, 1960; Boelter, 1965]. This anisotropycan be observed also in the vertical direction: when the fluxof water is upward, the peat can present a slightly highersaturated conductivity than when it is downward oriented[Myers, 1999]. Although the two assumptions of homoge-neity and isotropy may appear too severe if applied to a purepeat, they can be adopted if the ash content is as elevated asin the sites under consideration and the soil is a mixturepeat/mineral soil with a small fraction of organic soil.[56] The scarcity of information in literature about Brooks

and Corey model parameters specific for peat and marlysoils and the extreme variability of these among differenttypes of organic soils, leads us to consider a wide range ofvariation for the pore size distribution index, m, and thebubbling pressure head, ys. In particular, in the sensitivityanalysis of the model to the soil parameters, a range from0.08 to 0.30 has been considered for m, while a range from−2 to −30 cm has been considered for ys, in the attempt tocover all the potential values relative to the three differentsites. Some recent research confirms the analogy betweenorganic and clayey soils; for example, Myers [1999]investigating peat characteristics within the Florida Ever-glades, states that organic matter in these soils, as well asclayey soils, is known to interact with water at a microscopiclevel through chemical and electrostatic forces. Moreover,as in clays, shrinking and swelling behavior in organic soilsmay show hysteretic behavior. The values of porosity for thethree sites derived from the relation porosity‐peat fractionby Myers [1999] are rather similar to those typical of siltyclay and clay loam [Rawls and Brakensiek, 1989]. The pore

size distribution index, m, for silty clay and clay loam, ac-cording to Rawls and Brakensiek [1989], is equal to 0.127and 0.194, respectively, that are then the values that onecould expect in the three sites under analysis, consideringthe analogy between clayey and organic soils. According tothe water retention curves found by Myers [1999] for someisolated wetlands of southern Florida, the bubbling pressurehead should be in the order of about −10 cm. Naasz et al.[2005] analyzed a peat by means of laboratory experi-ments (using the Instantaneous Profile Method) during awetting‐drying cycle. The same authors provide two pairs ofparameters for the van Genuchten retention model; one isrelative to the wetting values while the other refers to thedrying ones. Assuming an average behavior, and thus usingmean parameter values between the two different pairsprovided by Naasz et al. [2005], the value of bubblingpressure head, ys, obtained after a procedure to convert vanGenuchten model parameters into Brooks and Corey modelparameters [Morel‐Seytoux et al., 1996], results equal to−9.19 cm, a value very close to that obtained by Myers[1999].

4. Analysis and Results

[57] The comparison between the model results and theobserved water table levels has been carried out in terms ofpdf’s of the water table depth as well as through the auto-correlation and power spectrum functions.[58] The model does not account for water levels above

the soil surface and describes fluctuations of the saturatedzone up to the soil surface which corresponds to finding thewater table at a depth ~y = ys. This is thus taken as the upperthreshold value (see section 2.1.1). The rare and short per-iods of submergence occurring at the considered sites arelimited to a few days per year, and have been ignored in theanalysis. Only the water table positions below the depth ys

have been then considered in the computation of theempirical distribution functions.[59] The annual analysis has been carried out with a set of

model input variables (rainfall parameters, potential evapo-transpiration, water levels into the canals) evaluated asannual average values from the daily time series. Themeasured time series are simultaneous only for a relativelyshort period of time and do not cover the whole time span ofthe water level measurements. However, since the aim ofthis work is to characterize the long‐term hydrologicalbehavior of the water table at the different sites, the entireseries of water level data has been used in the analysis. Theseasonal analysis has been carried out by splitting the annualtime series into two seasons (i.e., computing the averageseasonal values for the daily depth of rainy days, the rate ofrainy day occurrences, the potential evapotranspiration andthe water surface position of the external water bodies). Theresulting seasonal model pdf’s are then compared with thedistributions of the observed water table depth for eachseason (i.e., seasonal empirical pdf’s).

4.1. Parameter Estimations and Model SensitivityAnalysis

[60] In order to perform a sensitivity analysis of the modelto the soil and vegetation parameters, the rainfall andevapotranspiration parameters reported in section 3.1 (Table 2)


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and the values of y0 in Table 3 (see section 3.2) are fixed foreach site.[61] The sensitivity analysis of the model to the model

vegetation parameter shows that the influence of b on thegeneral behavior of the model pdf’s of water table depth israther weak and it decreases as the saturated hydraulic con-ductivity increases, while it is practically constant as the othersoil parameters (i.e., porosity, pore size distribution, bubblingpressure head) change. For ks within the range of potentiallysuitable values for the considered sites (i.e., ks = 10–35 cm/d,as it will be shown below), b has only a marginal impact onthe model pdf of water table depth, with pdf’s very similarwith each other for b ranging from 1 to 15 cm and onlyslightly shifted toward deeper positions of the water table forb ranging from 15 to a very high value such as 100 cm.[62] The sensitivity analysis of the model to the soil

parameters is performed using a Monte Carlo methodthrough the consideration of many different combinations ofthe four soil parameters (i.e., n, ks, m and ys), each onerandomly chosen within the ranges pointed out in section3.4. For each of these combinations, the parameter kl isobtained through the procedure described in section 3.2. Thevegetation parameters used here are those described insection 3.3 (Table 4).[63] Each simulation, relative to a set of soil parameters,

yields a pdf of the water table depth whose values of mean

(mmod), median (mdmod), standard deviation (smod), andskewness (g1

mod), are also computed. These statistics arethen compared to those computed from the empirical pdf(i.e., mobs, mdobs, sobs, g1

obs) obtaining the values of Dm(∣ mmod − mobs∣),Dmd (∣mdmod −mdobs∣),Ds (∣smod − sobs∣)and Dg1 (∣g1mod − g1

obs∣).[64] An example of the results of the sensitivity analysis is

shown in Figure 5; the four plots report the values of Dm,Dmd, Ds, and Dg1 (computed at the annual scale) as afunction of ys. The lowest deviations of all the model sta-tistics from the empirical ones are obtained with combina-tions of soil parameters having values of ys ranging from −8to −15 cm. In particular, the differences between theskewness coefficients are strongly correlated to ys, showingan almost linear behavior with decreasing values of Dg1 asys increases.[65] Moreover the sensitivity analysis shows that the

model results are more sensitive to ks and ys than to n andm, especially with regards to the seasonal parameterization.Analyzing the relations of Dm as a function of the four soilparameters, one can notice that most of the combinations ofsoil parameters with low values of Dm are characterized byvalues of ys and ks concentrated in quite narrow rangeswhile the corresponding ranges of n and m are rather wide.[66] Similar considerations can be made by observing

Figure 6 that shows the model pdf’s of water table depthobtained for Site 3, changing one soil parameter at a timeand keeping the other three unchanged. In particular, fivedifferent values chosen within the ranges provided in section3.4 are analyzed for each parameter. Once again the modelis more sensitive to ks and ys than it is to n and m. Despitethe wide ranges chosen, the model pdf’s obtained by usingdifferent values of n and m, maintain similar central loca-tion, dispersion and shape. When varying ks it can benoticed that the different pdf’s obtained for ks < 30 cm/d arerather different with each other, while they are rather similarfor higher values of the saturated hydraulic conductivity.This is a consequence of the fact that for relatively low

Table 4. Vegetation Parameters and Best Combinations of SoilParameters m, ks, n, and ys for Sites 1, 2, and 3

Site 1 Site 2 Site 3

Vegetation type mangrove sawgrass sawgrassAverage rooting depth, b (cm) 12 10 10Soil type peat marl marly peatPore size dist. index, m 0.154 0.126 0.188Sat. hydr. conduc., ks (cm/d) 13.16 34.17 32.87Porosity, n 0.514 0.542 0.518Bubbl. pres. head, ys (cm) −12.46 −11.52 −17.21

Figure 5. Values of the differences between the statistics derived from the annual model pdf’s ofwater table depth and the annual empirical pdf as a function of ys (cm): (top left) Dm (cm), (top right)Dmd (cm), (bottom right) Dg1, and (bottom left) Ds (cm). Only 500 combinations of the soil para-meters for Site 1 are shown.


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values of ks (e.g., 1 cm/d and 10 cm/d) both the SWT andDWT regimes are present while for higher values of ks (e.g.,20, 30 and 40 cm/d) only the SWT regime is present. Ananalogous situation can be noticed when varying ys; in thiscase the pdf’s relative to ys = −6 and −12 cm show thepresence of both the SWT and DWT regimes while the pdf’srelative to the other three values of ys tested are charac-terized by the presence of the only SWT regime.[67] Starting from 20,000 different combinations of the

four soil parameters, the “best” fit parameters for each sitehave been determined by filtering the results according tothe best agreement between the model and the empiricalpdf’s in terms of their statistics (at both the annual and theseasonal levels). The most important comparison parameterbetween the model and the empirical pdf’s is the centrallocation, second the dispersion and, finally, the shape. Thus,the values of Dm, Dmd, Ds and Dg1 have been considered,assigning decreasing importance to each of them. Thenumerical procedure used to determinate for each site the 20best combinations of soil parameters from the 20,000combinations initially analyzed is described in detail inauxiliary material Text S1.1

[68] From the analysis of the best 20 combinations of soilparameters, one can derive some information useful todetect the set of soil parameters by which the modelreproduce the empirical distributions more accurately, herereferred to as the “best combination” for each site. Despitethe use of relatively wide ranges for the four soil parametersat the beginning of the procedure (i.e., the ranges pointedout in section 3.4), the parameters relative to the resultingbest 20 combinations converge in very narrow ranges. Forexample, most of the 20 best combinations of Site 1 show avalue of ys from −12.29 to −12.49 cm, n from 0.5 to 0.527and m from 0.146 to 0.167. For Site 2, the ranges found are:ks from 31.1 to 34.2 cm/d, n from 0.541 to 0.547 and ys

from −11.4 to −15.7 cm. For Site 3, one can notice that mostof the 20 best combinations have m ranging from 0.168 to0.188, ks from 32 to 34.8 cm/d, n from 0.508 to 0.529 andys from −17.2 cm to −18 cm. Following the above con-siderations, for each site, the “best combination” of the soilparameters has been chosen among the 20 best combina-tions previously selected (Table 4).

4.2. Annual Analysis

[69] Figure 7 shows the results for the annual analysisobtained by using as soil parameters at each site the valuesreported in Table 4. It shows for the three different sites a

Figure 6. Sensitivity of the model to the four soil parameters for Site 3. (top left) n ranging from 0.40 to0.56, other model parameters corresponding to those of the best combination for Site 3 (Table 4). (topright) ks ranging from 1 to 40 cm/d, other parameters from the best combination for Site 3. (bottom left) mranging from 0.10 to 0.30, other parameters from the best combination for Site 3. (bottom right) ys

ranging from −6 to −30 cm, other parameters from the best combination for Site 3. Common parametersare those of climate (a, l, and PET) and y0, from the annual parameterizations for Site 3.

1Auxiliary material files are available in the HTML. doi:10.1029/2009WR008911.


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qualitative comparison between the model pdf’s of watertable depth and the empirical ones at the annual scale. Thewater table depths are reported in cm with respect to the soilsurface at each site.[70] One notices that for Site 1 (Figure 7a) the mode of

the model pdf is shifted toward a deeper groundwaterposition compared to the empirical pdf, while for the othertwo sites (Figures 7b and 7c) the modes of the model andempirical pdf’s are very close. Table 5 provides a quanti-

tative comparison showing that for Site 1 Dm is about 5 cm,while for the other two sites the values of Dm are around1 mm. Regarding the dispersion, the values of s relative tothe model and the empirical pdf’s are almost the same in thecase of Site 1 while they differ more markedly for the othertwo sites (Ds is only 0.04 cm for Site 1, while it is around4–5 cm for Site 2 and 3, Table 5).[71] The shapes of the model and empirical pdf’s are

rather similar for Site 1 (Figure 7a), while they present some

Figure 7. Annual analysis. Pdf’s of the water table depth obtained from the model (using soil parameterscorresponding to the best combinations in Table 4) compared to the empirical pdf’s of the water table for(a) Site 1, (b) Site 2, and (c) Site 3.


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differences at Site 2, where the empirical pdf appearsbimodal (Figure 7b). From Table 1, one can note that thedifference between the mean seasonal depths of the watertable during the dry and the wet season at Site 2 is almosttwo times that of Site 1. This could be physically explainedby the presence of a nearby canal, where the mean waterlevels during the wet and the dry seasons are at consistentlydifferent positions (see Table 3). This fact leads to differentlateral flow contributions during the two seasons that,obviously, affect the water table positions at the seasonalscale, and, as a consequence, also at the annual scale. Fromthe analysis of the historical data of water table for Site 2(section 2.3) one can note that after removing the seasonalityfrom the original series, the “detrended” series of waterlevels still presents a strong signal in the ACF (Figure 4b,middle) due to the influence of the nearby canal on the watertable dynamics. This confirms that the canals subject tohuman management may considerably impact the naturaldynamics of the water table. Analogous considerationscould be applied for Site 3, whose nearest water body is alsoa canal. In fact, the empirical pdf of Site 3 (Figure 7c) alsoshows a weak impact of seasonality, with a slight bimodalshape, even if this behavior is much less marked than in thecase of Site 2. The fact that the empirical pdf’s of Site 2 andSite 3 show bimodal features may also result from theirdifferent soil properties (such as the hydraulic conductivity)with respect to those relative to Site 1. In fact, the saturatedhydraulic conductivities for Sites 2 and 3, according to theresults of the procedure discussed above (section 4.1) isalmost three times that relative to Site 1 (see Table 4) andthis would makes the water table dynamics faster at thesetwo sites, thus emphasizing the effects of the seasonal cli-matic variability on the water table fluctuations.[72] The model, working at the annual scale, considers a

water level in the external canals to be constant and equal tothe annual mean. For this reason, it is not able to take intoaccount the difference in the seasonal contributions of thelateral flow. Moreover, the use of climatic parameters atthe annual scale leads the model to reduce the effect of theseasonal climatic variability.

[73] In Table 5, the values of the statistics relative to theobserved series and those arising from the model pdf’s arealso shown. It can be noted that, at the annual scale and forall the sites, the model mean and medians values are alwaysslightly lower than those observed (i.e., the mean andmedian positions of the water table derived from the modelare deeper than that observed). The values of the standarddeviation from the model are rather similar to thoseobserved, with differences always lower than 5.5 cm, even ifthere is some consistent underestimation. This means thatthe model underestimates the variability of the observedprocess (except for Site 1, where the annual model standarddeviation is almost the same as the observed one). FromTable 5 it can be also noted that, at the annual scale, theempirical distributions are rather skewed to the left (nega-tively skewed) for all the three site (especially at Site 2)while the model pdf’s for Site 2 and 3 are rather symmetric,and only at Site 1 a slight positive asymmetry can benoticed.

4.3. Seasonal Analysis

[74] As shown in Table 2, the wet season is characterizedby more intensive and frequent rainfall events, with a totalamount of precipitation near three times the values of thedry season. Thus a higher amount of water infiltrates the soilbut, at the same time, there is a higher rate of evapotrans-piration. The resulting water table is shallower during thewet season (see Table 1) and all the observed periods ofsubmergence occur during this season (see Figure 3).Moreover, during the dry season, the water table fluctuatesthrough a wider range of depths than during the wet seasonbecause of the prolonged dry period from December to May.[75] Table 5 reports some of the quantitative results of the

seasonal analysis, while Figure 8 shows a qualitative com-parison between the seasonal pdf’s resulting from the modeland the empirical data.[76] The model results at a seasonal level are not as

accurate as at the annual level, especially for the dry season.This is mainly evident at Sites 2 and 3 (Figures 8b and 8c),while the model performs better at Site 1 (Figure 8a). For allthe sites, the model pdf’s of water table shift toward shal-

Table 5. Statistics, at Both the Annual and the Seasonal Scale, Derived From the Empirical Pdf’s (Observed) and the Model Pdf’s(Modeled) Obtained by Using the Soil Parameters in Table 4a

Site

Observed Modeled

Dm (cm) Dmd (cm) Ds (cm) Dg1m (cm) md (cm) s (cm) g1 m (cm) md (cm) s (cm) g1

Annual1 −30.3 −29.8 8.7 −0.22 −35.6 −36.7 8.8 0.20 5.4 6.9 0.0 0.422 −44.6 −40.1 18.2 −0.62 −44.7 −45.3 13.8 −0.02 0.1 5.2 4.4 0.593 −52.1 −51.6 19.5 −0.43 −52.1 −52.9 14.0 0.03 0.1 1.3 5.6 0.46

Dry Season1 −34.6 −34.7 7.9 0.03 −40.0 −41.5 8.6 0.51 5.4 6.8 0.8 0.472 −54.8 −56.3 16.2 −0.07 −68.3 −70.5 12.2 0.82 13.5 14.2 4.0 0.893 −61.3 −61.4 18.5 −0.10 −83.2 −85.3 12.2 0.82 22.0 23.9 6.3 0.92

Wet Season1 −25.4 −25.2 6.9 −0.37 −24.9 −25.2 5.7 −0.21 0.5 0.0 1.0 0.172 −34.1 −31.9 13.7 −1.94 −34.0 −33.6 11.2 −0.41 0.1 1.7 2.5 1.533 −41.0 −40.3 14.3 −0.72 −37.1 −37.0 9.6 −0.37 3.8 3.4 4.7 0.35

aMean, m; median, md; standard deviation, s; skewness, g1.Dm = ∣mmod − mobs∣ in cm;Dmd = ∣mdmod − mdobs∣ in cm;Ds = ∣smod − sobs∣ in cm;Dg1 =∣g1mod − g1

obs∣.


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lower values during the wet season and toward deepervalues during the dry season. This behavior is probably dueto the dependency of the water table position to the initialcondition at the beginning of each season, rather than to themodel parameters for the season itself. The initial conditionis expected to play an important role, especially when thedifferences between the two seasons are marked, and itcannot be accounted for by the model which represents onlya steady state statistical condition.

[77] The persistence of a shallow water table at the end ofthe wet season and the relatively slow dynamics of the watertable, influence the water table depth over almost the entiredry season. Similarly, the initial condition at the beginningof the wet season influences the water table position duringthe period from June to November but, because the rainfallevents are more frequent and intense, it is likely that asteady condition is reached earlier than for the case of thedry season. This explains the fact that the model performsbetter for the wet season. Table 5 shows that during the dry

Figure 8. Seasonal analysis. Pdf’s of the water table depth obtained from the model (using soil para-meters corresponding to the best combinations in Table 4) compared to the empirical ones for (a) Site 1,(b) Site 2, and (c) Site 3. For each site are shown (top) the dry season (from December to May) and(bottom) the wet season (from June to November).


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season the values of mean and median derived from themodel are lower (i.e., deeper positions) than those derivedfrom the empirical pdf’s, especially for Sites 2 and 3 (thedifferences Dm and Dmd are on the order of 6 cm for Site 1,14 cm for Site 2 and 22 cm for Site 3). The central locationof the model pdf’s relative to the wet season is very close tothat of the correspondent empirical pdf’s for Sites 1 and 2,while for Site 3 the model mean and median are about3.5 cm higher than the observed ones. Another reason that, ina minor way, could affect the model accuracy in the seasonalreproduction of the water table dynamics during the dryseason is that when the water flow is oriented upward, thesoil at the three sites may have an upward hydraulic con-ductivity higher than the one downward (Myers, 1999). Suchbehavior which may enhance the ability of wetlands tomaintain a shallow water table is not represented in theanalytical model.[78] Although in the seasonal analysis the model takes

into account the different seasonal contributions of the lat-eral flow, by considering two different water levels into thecanals (one for each season, that is equal to the mean sea-sonal position), the presence of canals as external waterbodies is also responsible for discrepancies between themodel and the empirical pdf’s of the water table. As in thecase of the annual analysis, the water surface of the externalwater body has been considered constant in time for eachseason, while, in reality, the water levels in the canals aresubjected to daily fluctuations which may increase the var-iability of water table position, and that the model is not ableto consider. As can be observed from Table 5, the variabilityof the process is better reproduced at Site 1 than in the othertwo sites. In fact, the values of standard deviation relative tothe model pdf’s, for both the dry and wet season, are ratherclose to those obtained from the observed series (with Dson the order of 1 cm), while for the other two sites the valuesof Ds are on the order of 2.5–4.5 cm for the wet season and4–6 cm for the dry season (with the higher values referring

to Site 3), with the model underestimating the variability ofthe observed process.

4.4. Comparison Between Observed and SyntheticWater Table Time Series

[79] Many species find their niche based on not only inthe frequency at which a certain depth is exceeded, but alsoin the duration of high saturation levels (i.e., how long aplant can endure oxygen stress). Thus it is interesting tostudy the autocorrelation and power spectrum functions ofthe synthetic series produced by the model and how theycompare with the observed ones. Besides their own intrinsicinterest these functions also control the crossing propertiesof the processes.[80] The autocorrelation and power spectrum of simulated

water table positions have been studied through the numer-ical integration of equation (2) with constant values of PETand y0 as it is assumed in the model (following the sameapproach as that of Pumo et al. [2008]). All the availablerainfall data (e.g., from 1/1/2002 to 9/30/2008) were used asinput to the model using the “best” combination of soil andvegetation parameters for Site 1 (see Table 4).[81] The resulting series of daily water table positions is

shown in Figure 9 which also shows the historical data atSite 1. These two series have been also compared throughtheir autocorrelation and power spectral characteristics. Thecomparison is shown in Figure 10 for both, the originalseries as well as their deseasonalized versions (in order toremove the seasonality, the same procedure as in section 2.3has been used).[82] From Figures 9 and 10 one can observe that although

there are differences in the second order properties betweenthe data and the synthetic series, they are similar in theirgeneral structure despite the necessary simplificationsincorporated in the model. Note that the ACFs and the PSFsshown in Figure 10 for the observed series (blue lines) areslightly different from those shown in Figure 4a; this is

Figure 9. (top) Daily rainfall series. (bottom) Comparison between the observed daily water table timeseries (blue) and the synthetic model generated series (red) obtained by numerical integration ofequation (2). Site 1 with observation period from 1 January 2002 to 30 September 2008.


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because the time span considered for the comparison withthe synthetic series (i.e., from 1/1/2002 to 9/30/2008) isshorter than that used previously (i.e., from 10/2/95 to 1/26/2009, that is the entire series available). Although similar intheir general structure it is observed that the synthetic seriesproduced by the model are more locally noisy than theobserved data.

5. Conclusions

[83] Considering the increasing attention devoted inrecent years to wetlands and groundwater‐dependent eco-systems, it is becoming increasingly important to developand test quantitative models for the analysis of such eco-systems. A recent ecohydrological model proposed by Laioet al. [2009] provides a probabilistic description of the watertable depths and fluctuations in groundwater‐dependentecosystems. The model is based on a simple process‐basedsoil water balance and provides an analytical description ofthe statistical structure of the water table levels. Since thismodel has never been applied to real cases, this paperrepresents a first test of such a model with field data.

[84] The model has been applied to three sites in theFlorida Everglades using both the annual and seasonalparameterizations. The resulting pdf’s of water table depthshave been compared to those resulting from the daily his-torical series recorded at each site. A sensitivity analysis ofthe model to some parameters has been also performed,showing how the model results are only slightly dependenton the vegetation parameter b (i.e., average rooting depth),while they are strongly dependent on the soil parameters,and in particular, on the bubbling pressure head (ys) andsaturated hydraulic conductivity (ks).[85] The annual analysis has shown the capability of the

model to reproduce the observed distribution, using meanannual values of rainfall depth and frequency, evapotrans-piration and water surface position of the nearest water bodyas input parameters. Since Sites 2 and 3 are characterized bythe presence of a nearby canal, where the water levels duringthe dry season are at consistently different position fromthose during the wet season, the empirical pdf’s of the watertable present a bimodal shape that the model is unable toreproduce at the annual scale. Using the seasonal parame-terization, the model still reproduces the observed pdf in Site1 quite well. For the other two sites, the seasonal pdf’s are

Figure 10. (top left) Comparison between the autocorrelation functions (ACF) for the original observedwater table series (blue) and the synthetic series (red). (top right) The ACFs of the detrended series afterthe removal of the seasonal cycle (ACF DS) for the observed (blue) and the synthetic (red) series. (bottomleft) Comparison between the power spectra functions (PSF) of the original observed (blue) and synthetic(red) series. (bottom right) Comparison between the PSFs for the detrended series (PSF DS) observed(blue) and synthetic (red). The synthetic series have been obtained by numerical integration ofequation (2). Site 1 with observation period from 1 January 2002 to 30 September 2008.


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strongly affected by the initial position of the water table atthe beginning of each season and the model is less accu-rately on the reproduction of the observed pdf’s. In partic-ular, during the dry season, the model pdf’s are shiftedtoward deeper values, while the pdf’s of the wet season areshifted toward shallower water table values. This effect ismuch more evident during the dry season, when reaching asteady state condition requires more time than that requiredduring the wet season.[86] The model results, in both the annual and seasonal

analysis, are affected by the assumption of an external watersurface constant in time, while specially the water level inthe canals are subjected to strong daily/seasonal fluctuationswhich may increase the variability of water table positions.[87] The discrepancies between the observed values and

the model results may be explained by the soil parameterschosen for the sites under consideration which have beenevaluated after an optimization procedure based on thesimilarity between the model and observed pdf’s statistics,rather than through field or laboratory analyses. Furthermore,the model assumes the soil is homogeneous and isotropicwhile organic soils, such as those of the Everglades, areknown to have an anisotropic and hysteretic behavior. Inaddition to this, the rainfall and evapotranspiration para-meters are estimated with time series shorter than those of thewater table depths, and might be not fully representative ofthe climatic conditions occurring throughout time.[88] In conclusion, the model at the annual level has

shown an acceptable ability to reproduce the probabilisticdescription of the water table dynamics for groundwater‐dependent ecosystems having limited hydroperiods. Thestudy of frequently submerged sites, such as it is commonlyfound in the Everglades, requires the explicit considerationof the dynamics of water levels above the soil surface. Thisis the most important direction of ongoing research.

[89] Acknowledgments. This work was funded by the NationalAeronautics and Space Administration NASA Cooperative AgreementNNX08BA43A (WaterSCAPES: Science of Coupled Aquatic Processesin Ecosystems from Space) and the National Science Foundation undergrant 0642517 (Co‐organization of River Basin Geomorphology and Veg-etation). The authors gratefully acknowledge the help of the U.S. Geolog-ical Survey (USGS) and the Everglades Depth Estimation Network(EDEN). Some of the data sets were provided by the Florida Coastal Ever-glades Long‐Term Ecological Research (LTER) Program.

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modeling belowground water table fluctuations in the everglades

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